Next we show that \(\hat{\Gamma }(X)\)  can detect the presence of nonsmooth points.
It is known that the norm on \(X\)  is smooth if and only if BJ orthogonality is right
additive in the sense that \(x\perp y_1\)  and \(x\perp y_2\)  always implies \(x\perp (y_1+y_2)\)  (see [1]}).
Below we provide another criterion for smoothness which does not rely on underlying additive structure.
